Question

11. ABCD is a quadrilateral. Prove that AB + BC + CD + DA > AC + BD​

Answer 1

Answer:

2(AB + BC + CA + AD) > 2(AC + BD)

⇒ 2(AB + BC + CA + AD) > 2(AC + BD)

⇒ (AB + BC + CA + AD) > (AC + BD)

Answer 2

ABCD is a quadrilateral and AC and BC are the diagonals

sum of two sides of triangle is greater than three sides of triangle

has considering the triangle ABC D come and b c d and c a d and b a d we get

AB + BC > AC

CD + AD > AC

AB +AD > BC

BC + CD > BD

adding all three in the above equation

2(AB+ BC+CA+AD) > 2(AC+BD)

=> [ AB+BC+CA+AB] > 2( AC+BC)

I hope this would help you (⊙_⊙)